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Birth and Death Processes with Neutral Mutations
Joint Authors
Richard, Mathieu
Lambert, Amaury
Champagnat, Nicolas
Source
International Journal of Stochastic Analysis
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-20, 20 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-12-31
Country of Publication
Egypt
No. of Pages
20
Main Subjects
Abstract EN
We review recent results of ours concerning branching processes with general lifetimes and neutral mutations, under the infinitely many alleles model, where mutations can occur either at the birth of particles or at a constant rate during their lives.
In both models, we study the allelic partition of the population at time t.
We give closed-form formulae for the expected frequency spectrum at t and prove a pathwise convergence to an explicit limit, as t→+∞, of the relative numbers of types younger than some given age and carried by a given number of particles (small families).
We also provide the convergences in distribution of the sizes or ages of the largest families and of the oldest families.
In the case of exponential lifetimes, population dynamics are given by linear birth and death processes, and we can most of the time provide general formulations of our results unifying both models.
American Psychological Association (APA)
Champagnat, Nicolas& Lambert, Amaury& Richard, Mathieu. 2012. Birth and Death Processes with Neutral Mutations. International Journal of Stochastic Analysis،Vol. 2012, no. 2012, pp.1-20.
https://search.emarefa.net/detail/BIM-481457
Modern Language Association (MLA)
Champagnat, Nicolas…[et al.]. Birth and Death Processes with Neutral Mutations. International Journal of Stochastic Analysis No. 2012 (2012), pp.1-20.
https://search.emarefa.net/detail/BIM-481457
American Medical Association (AMA)
Champagnat, Nicolas& Lambert, Amaury& Richard, Mathieu. Birth and Death Processes with Neutral Mutations. International Journal of Stochastic Analysis. 2012. Vol. 2012, no. 2012, pp.1-20.
https://search.emarefa.net/detail/BIM-481457
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-481457